I had very similar goals when I started down this path a few years back. I was shooting a carbon barreled fierce in 300 WM. With a 26" barrel, added brake, I felt it was just too long to be carrying. Was an awesome shooter, but the barrel rise after the shot from recoil was just too much for me. The recoil per say was fine, as I could sit and shoot 20 ish plus rounds from the bench with no sore shoulder, but when in the field the barrel jump was more than necessary.
That is when I decided to go a custom rifle in 6.5 PRC. Almost the same ballistics as the 300 WM, but with less recoil. I pieced it together the way I wanted it, with the components I wanted, and I'm happy with it. I practice with it out to 1000m on a regular basis, but now have a dedicated bench rifle for fun that I use more for trigger time with a 6.5 CM. There are many more than capable calibers to go with these days, its just a matter of weighing out component availability, (brass), bullet availability and how much felt recoil you want in the end to get you with a decent amount of umph out at distance. Yes bullet placement is important in the end, but you have to have enough energy out there as well for the bullet to do its thing.
My specs: and I realize this is not for everyone, just what I wanted and did.
Defiance anti X short action, 22" proof carbon barrel, non threaded end, XLR carbon magnesium chassis, 4-20 ZCO scope. Rifle loaded sits just over the 9 lbs mark. Easy to carry, nice to shoot with less recoil and muzzle jump then the fierce was.
I went all out on the optic, as I hate not being able to see what I shoot at, at the most of trying times, first light, last light. Yes I have had instances at last light, or even first light with fog that through my optic was able to discern the game was non shooter, that others with lesser optics would not have had that ability. This is a personal choice to go a bit lighter of rifle, and a bit heavier optic and still be at an acceptable overall weight. My pet peeve is hearing or even running into it myself that you spend all this time and money and effort to get into game, and then not be able to discern if it is a shooter and have it walk away from you. Yes I have had this happen too often in my younger years to know that I did not want it to keep happening. Sometimes that extra 10-15 min of usable light that the better optics allow you to get is worth it, again everyone has a choice there.